How do i prove if this is true or false?

Question

Is $\mathcal{P}(A\cup B)=\mathcal{P}(A)\cup\mathcal{P}(B)$ true for all sets $A$ and $B$? If so, prove it. If not, give an example of sets $A$ and $B$ for which it is false and show why it is false for these sets.

What have you tried? $A$ and $B$ can be rather small, so trying some small cases should suffice. — Ross Millikan, Apr 29 '20 at 03:54
yea i got it now cause i used a smaller set. was using quite large sets before and it was really tedious — Wesley Fung, Apr 29 '20 at 04:11

score 1 · Answer 1 · answered Apr 29 '20 at 04:04

1

Suppose $A$ and $B$ are disjoint. Does $2^{a+b}=2^a+2^b-1$ for integers $a,b \ge 0$ ?

answered Apr 29 '20 at 04:04

gandalf61

15,326

where does the -1 come from? – J. De Ro Apr 29 '20 at 07:24
@ε-δ Even if $A$ and $B$ are disjoint, $\mathcal{P}(A)$ and $\mathcal{P}(B)$ have one element in common ... – gandalf61 Apr 29 '20 at 09:01
Yes, of course. Thanks! – J. De Ro Apr 29 '20 at 09:07

How do i prove if this is true or false?

1 Answers1